On statistical testing of composite hypotheses on $s$-dimensional uniform probability distribution of binary sequences

Yu. S. Kharin ; A. M. Zubkov

Diskretnaya Matematika, Tome 36 (2024) no. 1, pp. 116-135

Résumé

A problem of construction and analysis of statistical decision rules for testing of composite hypotheses on $s$-dimensional uniform probability distribution of binary random sequences is considered. An adequate for applications model of composite null hypothesis $H_0^{\varepsilon}$ with some fixed maximal deviation $\varepsilon$ from the uniform distribution is proposed. An approach to construction of a test for composite hypotheses $H_0^{\varepsilon}$, $\overline{H_0^{\varepsilon}}$ based on asymptotic expansion (w.r.t. $\varepsilon\rightarrow 0$) of the logarithmic probability ratio statistic is developed. The consistent test with a fixed significance level is constructed and its power is analyzed theoretically and by computer experiments.

Détail

Keywords: statistical test, binary sequence, $s$-dimensional uniformity, composite hypotheses, asymptotic expansion, consistency.

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